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Remark on bilinear operations on tensor fields. (English) Zbl 07285967
Summary: This short note completes the results of [J. Janyška, Arch. Math., Brno 55, No. 5, 289–308 (2019; Zbl 07144744)] by removing the locality assumption on the operators. After providing a quick survey on (infinitesimally) natural operations, we show that all the bilinear operators classified in [loc. cit.] can be characterized in a completely algebraic way, even without any continuity assumption on the operations.
MSC:
58A32 Natural bundles
53A55 Differential invariants (local theory), geometric objects
58A20 Jets in global analysis
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References:
[1] Čap, Andreas; Slovák, Jan, Infinitesimally natural operators are natural, Differential Geom. Appl. 2 (1) (1992), 45-55
[2] Čap, Andreas; Slovák, Jan, On multilinear operators commuting with Lie derivatives, Ann. Global Anal. Geom. 13 (3) (1995), 251-279
[3] Janyška, Josef, Remarks on natural differential operators with tensor fields, Arch. Math. (Brno) 55 (2019), 289-308
[4] Kolář, Ivan; Michor, Peter W.; Slovák, Jan, Natural operations in Differential Geometry, Springer, 1993, vi+434 pp
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